The natural volume method (NVM): Presentation and application to shallow water inviscid flows

In this paper a fully Lagrangian formulation is used to simulate 2D shallow water inviscid flows. The natural element method (NEM), which has been used successfully with several solid and fluid mechanics applications, is used to approximate the fluxes over Voronoi cells. This particle-based method hats shown huge potential in terms of handling problems involving large deformations. Its main advantage lies in the interpolant. character of its shape function and consequently the ease it allows with respect to the imposition of Dirichlet boundary conditions. In this paper, we use the NEM collocationally, and in a Lagrangian kinematic description, in order to simulate shallow grater flows that are boundary moving problems. This formulation is ultimately shown to constitute a unite-volume methodology requiring at flux computation on Voronoi cells rather than the standard elements, in a triangular or quadrilateral mesh. St Venant equations are used as the mathematical model. These equations-have discontinuous solutions that physically represent the existence of shock waves, meaning that stabilization issues have thus been considered. An artificial viscosity deduced from,in analogy with Riemann solvers is introduced to upwind the scheme and therefore stabilize the method. Some inviscid bidimensional flows were used as preliminary benchmark tests, which produced decent results, leading to well-founded hopes for the future of this method in real applications. Copyright (C) 2008 John Wiley & Sons, Ltd.